Musculoskeletal pain is common. Because pain is subjective, objectively describing it is crucial. However, pain assessment may cause distress in patients;therefore, physical therapists (PTs) should conduct these tests...Musculoskeletal pain is common. Because pain is subjective, objectively describing it is crucial. However, pain assessment may cause distress in patients;therefore, physical therapists (PTs) should conduct these tests quickly and accurately. Simple and clear instructions are recommended for pain assessment. However, few studies have provided evidence to support this hypothesis. Correspondingly, this study aimed to confirm the effectiveness of specific verbal instructions for pain location during five consecutive Passive Straight Leg Raise (PSLR) tests. The 28 asymptomatic participants (age 27.4 ± 9.6 years) who provided informed consent received five consecutive PSLR tests: three without and two with specific verbal instructions to ascertain pain intensity, quality, and location. The participants drew pain locations on a body chart and described the pain intensity and quality after each test. All participants were interviewed regarding the differences they noted in the presence and absence of specific verbal instructions. Each pain location was classified into one of ten areas for statistical analysis. The proportion of participants who changed the pain location was compared between the tests using McNemar’s test, and the kappa coefficient was confirmed for consistency of pain location. There was a significant difference in the proportion of participants who changed their pain location between the second and third tests and from the third to the fourth test (McNemar’s test: p = 0.003). Kappa coefficients had low consistency (κ = 0.28) just after receiving the specific verbal instructions in the fourth test compared to the third test. Consistency improved in the fifth test (κ = 0.57);93% of the participants answered that the pain location had become clearer. This study revealed the effects of specific verbal instructions in identifying pain locations. This detailed information may help PTs provide appropriate treatment and contribute to reducing pain in clinical settings.展开更多
With a pair of antennas spaced apart, an airborne passive location system measures phase differences of emitting signals. Regarded as cyclic ambiguities, the moduli of the measurements traditionally are resolved by ad...With a pair of antennas spaced apart, an airborne passive location system measures phase differences of emitting signals. Regarded as cyclic ambiguities, the moduli of the measurements traditionally are resolved by adding more antenna elements. This paper models the cyclic ambiguity as a component of the system state, of which the observability is analyzed and compared to that of the bear- ings-only passive location system. It is shown that the necessary and sufficient observability condition for the bearings-only passive location system is only the necessary observability condition for the passive location system with phase difference measurements, and that when the system state is observable, the cyclic ambiguities can be estimated by accumulating the phase difference measurements, thereby making the observer able to locate the emitter with high-precision.展开更多
In order to improve the performance of the traditional hybrid time-of-arrival(TOA)/angle-of-arrival(AOA)location algorithm in non-line-of-sight(NLOS)environments,a new hybrid TOA/AOA location estimation algorith...In order to improve the performance of the traditional hybrid time-of-arrival(TOA)/angle-of-arrival(AOA)location algorithm in non-line-of-sight(NLOS)environments,a new hybrid TOA/AOA location estimation algorithm by utilizing scatterer information is proposed.The linearized region of the mobile station(MS)is obtained according to the base station(BS)coordinates and the TOA measurements.The candidate points(CPs)of the MS are generated from this region.Then,using the measured TOA and AOA measurements,the radius of each scatterer is computed.Compared with the prior scatterer information,true CPs are obtained among all the CPs.The adaptive fuzzy clustering(AFC)technology is adopted to estimate the position of the MS with true CPs.Finally,simulations are conducted to evaluate the performance of the algorithm.The results demonstrate that the proposed location algorithm can significantly mitigate the NLOS effect and efficiently estimate the MS position.展开更多
Technology of passive location has broad prospects inapplications. In this paper, the sin- gle observer passive locationmethod using phase rate of change is introduced based on existingmeth- ods. This new method can o...Technology of passive location has broad prospects inapplications. In this paper, the sin- gle observer passive locationmethod using phase rate of change is introduced based on existingmeth- ods. This new method can obtain the direction of he target withphase information of two orthogonal interferometers on the observerand the radial distance with the corresponding phase rate of change.Then the target can be located with high speed and precision. Somelocating expressions are given When the flying posture of theobserver is change. Simulations show that this method is effective.展开更多
The conventional mono-station passive location techniques of direction finding are low in speed and accuracy, due to the little information available. In this paper, a novel measurement-rate (derivative) of phase diff...The conventional mono-station passive location techniques of direction finding are low in speed and accuracy, due to the little information available. In this paper, a novel measurement-rate (derivative) of phase difference from a two-element antenna array (interferometer) is introduced, accuracy of a passive location system with this measurement and directions of arrival (DOA) is analyzed, and the Cramer-Rao bound of location error of this system for 3D location is examined by simulations.展开更多
Under the scenario of dense targets in clutter, a multi-layer optimal data correlation algorithm is proposed. This algorithm eliminates a large number of false location points from the assignment process by rough corr...Under the scenario of dense targets in clutter, a multi-layer optimal data correlation algorithm is proposed. This algorithm eliminates a large number of false location points from the assignment process by rough correlations before we calculate the correlation cost, so it avoids the operations for the target state estimate and the calculation of the correlation cost for the false correlation sets. In the meantime, with the elimination of these points in the rough correlation, the disturbance from the false correlations in the assignment process is decreased, so the data correlation accuracy is improved correspondingly. Complexity analyses of the new multi-layer optimal algorithm and the traditional optimal assignment algorithm are given. Simulation results show that the new algorithm is feasible and effective.展开更多
To solve the problem of multiple moving sources passive location, a novel blind source separa- tion (BSS) algorithm based on the muhiset canonical correlation analysis (MCCA) is presented by exploiting the differe...To solve the problem of multiple moving sources passive location, a novel blind source separa- tion (BSS) algorithm based on the muhiset canonical correlation analysis (MCCA) is presented by exploiting the different temporal structure of uncorrelated source signals first, and then on the basis of this algorithm, a novel multiple moving sources passive location method is proposed using time difference of arrival (TDOA) and frequency difference of arrival (FDOA) measurements. The key technique of this location method is TDOA and FDOA joint estimation, which is based on BSS. By blindly separating mixed signals from multiple moving sources, the multiple sources location problem can be translated to each source location in turn, and the effect of interference and noise can also he removed. The simulation results illustrate that the performance of the MCCA algorithm is very good with relatively light computation burden, and the location algorithm is relatively simple and effective.展开更多
Technology of passive location has broad prospects in applications. In this paper, the method using the phase rate of change for the single observer passive location is introduced based on existing methods. One can ob...Technology of passive location has broad prospects in applications. In this paper, the method using the phase rate of change for the single observer passive location is introduced based on existing methods. One can obtain the direction of the target with phase information of two orthogonal interferometers on the observer and the radial distance with the corresponding phase rate of change. Then the target can be located with high speed and precision. A locating approach is given when the flying posture of t...展开更多
The two-station positioning system based on time difference and azimuth measurement has measurement redundancy. Therefore, not only can a positioning solution which is completely independent of the baseline length bet...The two-station positioning system based on time difference and azimuth measurement has measurement redundancy. Therefore, not only can a positioning solution which is completely independent of the baseline length between two stations be derived, but also the baseline length can be solved as an unknown quantity. These findings not only enhance the performance of the two-station positioning system, but also provide a design basis for the construction of a self-organizing dynamic intelligent positioning system.展开更多
This paper presents a Doppler passive location method for moving targets with fixed single station using the Doppler frequency shift and time difference information.First,based on the relationship between frequency sh...This paper presents a Doppler passive location method for moving targets with fixed single station using the Doppler frequency shift and time difference information.First,based on the relationship between frequency shift and path difference,the virtual path difference is calculated from the measured value of Doppler frequency shift by means of mean value correction.Then,under the assumption that the target is moving at a constant speed along a straight line,two coaxial virtual double base arrays are constructed by using the moving track of the moving target based on the method of fixed period time difference.On this basis,the moving distance of the moving target can be calculated by using the ratio relationship between the frequency difference and the radial distance between the two adjacent detection points in the middle of the array,and the linear solution of the two double base path difference positioning equations.At this point,the relative coordinate position of the moving target can be obtained by directly using the linear solution of the double base path difference positioning equation again.展开更多
Analyzed the relation between time delay difference and time delay estimation errors, based on the principles of three-point locating, a reformed threshold method for time delay difference estimation of impulse signal...Analyzed the relation between time delay difference and time delay estimation errors, based on the principles of three-point locating, a reformed threshold method for time delay difference estimation of impulse signals, called as amendment estimation for short, is developed by introducing channel equalization technique to its conventional version, named as direct estimation in this paper, to improve the estimation stability. After inherent relationship between time delay and phase shift of signals is analyzed, an integer period error compensation method utilized the diversities of both contribution share and contribution mode of concerned estimates is proposed under the condition of high precision phase lag estimation. Finally, a cooperative multi-threshold estimation method composed of amendment and direct estimations to process impulse signals with three thresholds is established. In sea trials data tests of passive locating, this method improves the estimation precision of time delay difference efficiently. The experiments verify the theoretical predictions.展开更多
For the joint time difference of arrival(TDOA) and angle of arrival(AOA) location scene,two methods are proposed based on the rectangular coordinates and the polar coordinates,respectively.The problem is solved pe...For the joint time difference of arrival(TDOA) and angle of arrival(AOA) location scene,two methods are proposed based on the rectangular coordinates and the polar coordinates,respectively.The problem is solved perfectly by calculating the target position with the joint TDOA and AOA location.On the condition of rectangular coordinates,first of all,it figures out the radial range between target and reference stations,then calculates the location of the target.In the case of polar coordinates,first of all,it figures out the azimuth between target and reference stations,then figures out the radial range between target and reference stations,finally obtains the location of the target.Simultaneously,simulation analyses show that the theoretical analysis is correct,and the proposed methods also provide the application of the joint TDOA and AOA location algorithm with the theoretical basis.展开更多
Based on the time differences of arrival(TDOA) and frequency differences of arrival(FDOA) measurements of the given planar stationary radiation source, the joint TDOA/FDOA location algorithm which solves the location ...Based on the time differences of arrival(TDOA) and frequency differences of arrival(FDOA) measurements of the given planar stationary radiation source, the joint TDOA/FDOA location algorithm which solves the location of the target directly is proposed. Compared with weighted least squares(WLS) methods,the proposed algorithm is also suitable for well-posed conditions,and gets rid of the dependence on the constraints of Earth's surface. First of all, the solution formulas are expressed by the radial range. Then substitute it into the equation of the radial range to figure out the radial range between the target and the reference station. Finally use the solution expression of the target location to estimate the location of the target accurately. The proposed algorithm solves the problem that WLS methods have a large positioning error when the number of observation stations is not over-determined. Simulation results show the effectiveness of the proposed algorithm, including effectively increasing the positioning accuracy and reducing the number of observatories.展开更多
Most existing studies about passive radar systems are based on the already known illuminator of opportunity(IO)states.However,in practice,the receiver generally has little knowledge about the IO states.Little research...Most existing studies about passive radar systems are based on the already known illuminator of opportunity(IO)states.However,in practice,the receiver generally has little knowledge about the IO states.Little research has studied this problem.This paper analyzes the observability and estimability for passive radar systems with unknown IO states under three typical scenarios.Besides,the directions of high and low estimability with respect to various states are given.Moreover,two types of observations are taken into account.The effects of different observations on both observability and estimability are well analyzed.For the observability test,linear and nonlinear methods are considered,which proves that both tests are applicable to the system.Numerical simulations confirm the correctness of the theoretical analysis.展开更多
For Time Difference Of Arrival(TDOA) location based on multi-ground stations scene,two direct solution methods are proposed to solve the target position in TDOA location.Therein,the solving methods are realized in the...For Time Difference Of Arrival(TDOA) location based on multi-ground stations scene,two direct solution methods are proposed to solve the target position in TDOA location.Therein,the solving methods are realized in the rectangular and polar coordinates.On the condition of rectangular coordinates,first of all,it solves the radial range between the target and reference station,then cal-culates the location of the target.In the case of polar coordinates,the azimuth between the target and reference station is solved first,then the radial range between the target and reference station is figured out,finally the location of the target is obtained.Simultaneously,the simulation and comparison analysis are given in detail,and show that the polar solving method has the better fuzzy performance than that of rectangular coordinate.展开更多
According to the existing research, the fault section location and fault location of passive distribution network and active distribution network are reviewed. Among them, fault location of passive distribution networ...According to the existing research, the fault section location and fault location of passive distribution network and active distribution network are reviewed. Among them, fault location of passive distribution network mainly introduces fault segment location based on transient state and steady state quantity and fault location based on transient quantity. The active distribution network mainly introduces the fault segment location based on the current amount and the switching capacity based on the distribution network topology. On this basis, the difficulties of fault location in the distribution network at present are analyzed, and the future development is prospected.展开更多
In this paper, the problem of underwater passive target motion analysis (TMA) in three dimensions is discussed using the measurements of passive bearings and elevation and frequency on the condition that acoustic sour...In this paper, the problem of underwater passive target motion analysis (TMA) in three dimensions is discussed using the measurements of passive bearings and elevation and frequency on the condition that acoustic source and observer are in different horizontal planes. Simulation results with both of the PLE (pseudo-linear estimation) and MLE (Maximum likelihood estimation) show that the TMA method is effective in oceanic environment. Its error covariance curves tend to its Cramer-Rao lower bounds.展开更多
文摘Musculoskeletal pain is common. Because pain is subjective, objectively describing it is crucial. However, pain assessment may cause distress in patients;therefore, physical therapists (PTs) should conduct these tests quickly and accurately. Simple and clear instructions are recommended for pain assessment. However, few studies have provided evidence to support this hypothesis. Correspondingly, this study aimed to confirm the effectiveness of specific verbal instructions for pain location during five consecutive Passive Straight Leg Raise (PSLR) tests. The 28 asymptomatic participants (age 27.4 ± 9.6 years) who provided informed consent received five consecutive PSLR tests: three without and two with specific verbal instructions to ascertain pain intensity, quality, and location. The participants drew pain locations on a body chart and described the pain intensity and quality after each test. All participants were interviewed regarding the differences they noted in the presence and absence of specific verbal instructions. Each pain location was classified into one of ten areas for statistical analysis. The proportion of participants who changed the pain location was compared between the tests using McNemar’s test, and the kappa coefficient was confirmed for consistency of pain location. There was a significant difference in the proportion of participants who changed their pain location between the second and third tests and from the third to the fourth test (McNemar’s test: p = 0.003). Kappa coefficients had low consistency (κ = 0.28) just after receiving the specific verbal instructions in the fourth test compared to the third test. Consistency improved in the fifth test (κ = 0.57);93% of the participants answered that the pain location had become clearer. This study revealed the effects of specific verbal instructions in identifying pain locations. This detailed information may help PTs provide appropriate treatment and contribute to reducing pain in clinical settings.
文摘With a pair of antennas spaced apart, an airborne passive location system measures phase differences of emitting signals. Regarded as cyclic ambiguities, the moduli of the measurements traditionally are resolved by adding more antenna elements. This paper models the cyclic ambiguity as a component of the system state, of which the observability is analyzed and compared to that of the bear- ings-only passive location system. It is shown that the necessary and sufficient observability condition for the bearings-only passive location system is only the necessary observability condition for the passive location system with phase difference measurements, and that when the system state is observable, the cyclic ambiguities can be estimated by accumulating the phase difference measurements, thereby making the observer able to locate the emitter with high-precision.
基金The National High Technology Research and Development Program of China(863Program)(No.2008AA01Z227)the National Natural Science Foundation of China(No.60872075)
文摘In order to improve the performance of the traditional hybrid time-of-arrival(TOA)/angle-of-arrival(AOA)location algorithm in non-line-of-sight(NLOS)environments,a new hybrid TOA/AOA location estimation algorithm by utilizing scatterer information is proposed.The linearized region of the mobile station(MS)is obtained according to the base station(BS)coordinates and the TOA measurements.The candidate points(CPs)of the MS are generated from this region.Then,using the measured TOA and AOA measurements,the radius of each scatterer is computed.Compared with the prior scatterer information,true CPs are obtained among all the CPs.The adaptive fuzzy clustering(AFC)technology is adopted to estimate the position of the MS with true CPs.Finally,simulations are conducted to evaluate the performance of the algorithm.The results demonstrate that the proposed location algorithm can significantly mitigate the NLOS effect and efficiently estimate the MS position.
文摘Technology of passive location has broad prospects inapplications. In this paper, the sin- gle observer passive locationmethod using phase rate of change is introduced based on existingmeth- ods. This new method can obtain the direction of he target withphase information of two orthogonal interferometers on the observerand the radial distance with the corresponding phase rate of change.Then the target can be located with high speed and precision. Somelocating expressions are given When the flying posture of theobserver is change. Simulations show that this method is effective.
文摘The conventional mono-station passive location techniques of direction finding are low in speed and accuracy, due to the little information available. In this paper, a novel measurement-rate (derivative) of phase difference from a two-element antenna array (interferometer) is introduced, accuracy of a passive location system with this measurement and directions of arrival (DOA) is analyzed, and the Cramer-Rao bound of location error of this system for 3D location is examined by simulations.
基金This project was supported by the National Natural Science Foundation of China (60672139, 60672140)the Excellent Ph.D. Paper Author Foundation of China (200237)the Natural Science Foundation of Shandong (2005ZX01).
文摘Under the scenario of dense targets in clutter, a multi-layer optimal data correlation algorithm is proposed. This algorithm eliminates a large number of false location points from the assignment process by rough correlations before we calculate the correlation cost, so it avoids the operations for the target state estimate and the calculation of the correlation cost for the false correlation sets. In the meantime, with the elimination of these points in the rough correlation, the disturbance from the false correlations in the assignment process is decreased, so the data correlation accuracy is improved correspondingly. Complexity analyses of the new multi-layer optimal algorithm and the traditional optimal assignment algorithm are given. Simulation results show that the new algorithm is feasible and effective.
基金Supported by the National High Technology Research and Development Program of China(No.2009AAJ116,2009AAJ208,2010AA7010422)the National Science Foundation for Post-Doctoral Scientists of China(No.20080431379,200902671)the Hubei Natural Science Foundation(No.2009CDB031)
文摘To solve the problem of multiple moving sources passive location, a novel blind source separa- tion (BSS) algorithm based on the muhiset canonical correlation analysis (MCCA) is presented by exploiting the different temporal structure of uncorrelated source signals first, and then on the basis of this algorithm, a novel multiple moving sources passive location method is proposed using time difference of arrival (TDOA) and frequency difference of arrival (FDOA) measurements. The key technique of this location method is TDOA and FDOA joint estimation, which is based on BSS. By blindly separating mixed signals from multiple moving sources, the multiple sources location problem can be translated to each source location in turn, and the effect of interference and noise can also he removed. The simulation results illustrate that the performance of the MCCA algorithm is very good with relatively light computation burden, and the location algorithm is relatively simple and effective.
文摘Technology of passive location has broad prospects in applications. In this paper, the method using the phase rate of change for the single observer passive location is introduced based on existing methods. One can obtain the direction of the target with phase information of two orthogonal interferometers on the observer and the radial distance with the corresponding phase rate of change. Then the target can be located with high speed and precision. A locating approach is given when the flying posture of t...
文摘The two-station positioning system based on time difference and azimuth measurement has measurement redundancy. Therefore, not only can a positioning solution which is completely independent of the baseline length between two stations be derived, but also the baseline length can be solved as an unknown quantity. These findings not only enhance the performance of the two-station positioning system, but also provide a design basis for the construction of a self-organizing dynamic intelligent positioning system.
文摘This paper presents a Doppler passive location method for moving targets with fixed single station using the Doppler frequency shift and time difference information.First,based on the relationship between frequency shift and path difference,the virtual path difference is calculated from the measured value of Doppler frequency shift by means of mean value correction.Then,under the assumption that the target is moving at a constant speed along a straight line,two coaxial virtual double base arrays are constructed by using the moving track of the moving target based on the method of fixed period time difference.On this basis,the moving distance of the moving target can be calculated by using the ratio relationship between the frequency difference and the radial distance between the two adjacent detection points in the middle of the array,and the linear solution of the two double base path difference positioning equations.At this point,the relative coordinate position of the moving target can be obtained by directly using the linear solution of the double base path difference positioning equation again.
文摘Analyzed the relation between time delay difference and time delay estimation errors, based on the principles of three-point locating, a reformed threshold method for time delay difference estimation of impulse signals, called as amendment estimation for short, is developed by introducing channel equalization technique to its conventional version, named as direct estimation in this paper, to improve the estimation stability. After inherent relationship between time delay and phase shift of signals is analyzed, an integer period error compensation method utilized the diversities of both contribution share and contribution mode of concerned estimates is proposed under the condition of high precision phase lag estimation. Finally, a cooperative multi-threshold estimation method composed of amendment and direct estimations to process impulse signals with three thresholds is established. In sea trials data tests of passive locating, this method improves the estimation precision of time delay difference efficiently. The experiments verify the theoretical predictions.
基金supported by the National Natural Science Foundation of China(6107210761271300)+4 种基金the Shaanxi Industry Surmount Foundation(2012K06-12)the Arm and Equipment Pre-research Foundationthe Fundamental Research Funds for the Central Universities of China(K0551302006K5051202045K50511020024)
文摘For the joint time difference of arrival(TDOA) and angle of arrival(AOA) location scene,two methods are proposed based on the rectangular coordinates and the polar coordinates,respectively.The problem is solved perfectly by calculating the target position with the joint TDOA and AOA location.On the condition of rectangular coordinates,first of all,it figures out the radial range between target and reference stations,then calculates the location of the target.In the case of polar coordinates,first of all,it figures out the azimuth between target and reference stations,then figures out the radial range between target and reference stations,finally obtains the location of the target.Simultaneously,simulation analyses show that the theoretical analysis is correct,and the proposed methods also provide the application of the joint TDOA and AOA location algorithm with the theoretical basis.
基金supported by the National Natural Science Foundation of China(6140236561271300)the 13th Five-Year Weaponry PreResearch Project。
文摘Based on the time differences of arrival(TDOA) and frequency differences of arrival(FDOA) measurements of the given planar stationary radiation source, the joint TDOA/FDOA location algorithm which solves the location of the target directly is proposed. Compared with weighted least squares(WLS) methods,the proposed algorithm is also suitable for well-posed conditions,and gets rid of the dependence on the constraints of Earth's surface. First of all, the solution formulas are expressed by the radial range. Then substitute it into the equation of the radial range to figure out the radial range between the target and the reference station. Finally use the solution expression of the target location to estimate the location of the target accurately. The proposed algorithm solves the problem that WLS methods have a large positioning error when the number of observation stations is not over-determined. Simulation results show the effectiveness of the proposed algorithm, including effectively increasing the positioning accuracy and reducing the number of observatories.
基金This work was supported by the National Natural Science Foundation of China(61803379)the China Postdoctoral Science Foundation(2017M613370,2018T111129).
文摘Most existing studies about passive radar systems are based on the already known illuminator of opportunity(IO)states.However,in practice,the receiver generally has little knowledge about the IO states.Little research has studied this problem.This paper analyzes the observability and estimability for passive radar systems with unknown IO states under three typical scenarios.Besides,the directions of high and low estimability with respect to various states are given.Moreover,two types of observations are taken into account.The effects of different observations on both observability and estimability are well analyzed.For the observability test,linear and nonlinear methods are considered,which proves that both tests are applicable to the system.Numerical simulations confirm the correctness of the theoretical analysis.
基金Supported by the National Natural Science Foundation of China (No. 60825104,61072107)the National Postdoctor Fundation (No. 20090451251)+1 种基金the Shaanxi Industry Surmount Foundation (2009K08-31)the Fundamental Research Funds for the Central Universities(JY10000-902025) of China
文摘For Time Difference Of Arrival(TDOA) location based on multi-ground stations scene,two direct solution methods are proposed to solve the target position in TDOA location.Therein,the solving methods are realized in the rectangular and polar coordinates.On the condition of rectangular coordinates,first of all,it solves the radial range between the target and reference station,then cal-culates the location of the target.In the case of polar coordinates,the azimuth between the target and reference station is solved first,then the radial range between the target and reference station is figured out,finally the location of the target is obtained.Simultaneously,the simulation and comparison analysis are given in detail,and show that the polar solving method has the better fuzzy performance than that of rectangular coordinate.
文摘According to the existing research, the fault section location and fault location of passive distribution network and active distribution network are reviewed. Among them, fault location of passive distribution network mainly introduces fault segment location based on transient state and steady state quantity and fault location based on transient quantity. The active distribution network mainly introduces the fault segment location based on the current amount and the switching capacity based on the distribution network topology. On this basis, the difficulties of fault location in the distribution network at present are analyzed, and the future development is prospected.
文摘In this paper, the problem of underwater passive target motion analysis (TMA) in three dimensions is discussed using the measurements of passive bearings and elevation and frequency on the condition that acoustic source and observer are in different horizontal planes. Simulation results with both of the PLE (pseudo-linear estimation) and MLE (Maximum likelihood estimation) show that the TMA method is effective in oceanic environment. Its error covariance curves tend to its Cramer-Rao lower bounds.